DG discretization of optimized Schwarz methods for Maxwell's equations

Mohamed El Bouajaji, Victorita Dolean, Martin J. Gander, Stéphane Lanteri, Ronan Perrussel

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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Abstract

We study here optimized Schwarz domain decomposition methods for solving the time-harmonic Maxwell equations discretized by a discontinuous Galerkin (DG) method. Due to the particularity of the latter, a discretization of a more sophisticated Schwarz method is not straightforward. A strategy of discretization is shown in the framework of a DG weak formulation, and the equivalence between multi-domain and single-domain solutions is proved. The proposed discrete framework is then illustrated by some numerical results through the simulation of two-dimensional propagation problems.
Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XXI
EditorsJocelyne Erhel, Martin J. Gander, Laurence Halpern, Géraldine Pichot, Taoufik Sassi, Olof Widlund
PublisherSpringer-Verlag
Pages217-225
Number of pages9
Volume98
ISBN (Electronic)9783319057897
ISBN (Print)9783319057880
DOIs
Publication statusPublished - 21 Apr 2014
Event21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014 - Rennes, France
Duration: 25 Jun 201229 Jun 2012

Publication series

NameLecture Notes in Computational Science and Engineering
Volume98
ISSN (Print)1439-7358

Conference

Conference21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014
CountryFrance
CityRennes
Period25/06/1229/06/12

Fingerprint

Schwarz Methods
Domain decomposition methods
Discontinuous Galerkin
Maxwell equations
Galerkin methods
Maxwell's equations
Discretization
Weak Formulation
Discontinuous Galerkin Method
Domain Decomposition Method
Harmonic
Equivalence
Propagation
Numerical Results
Simulation
Framework
Strategy

Keywords

  • dg
  • Schwarz methods
  • Maxwell equations

Cite this

El Bouajaji, M., Dolean, V., Gander, M. J., Lanteri, S., & Perrussel, R. (2014). DG discretization of optimized Schwarz methods for Maxwell's equations. In J. Erhel, M. J. Gander, L. Halpern, G. Pichot, T. Sassi, & O. Widlund (Eds.), Domain Decomposition Methods in Science and Engineering XXI (Vol. 98, pp. 217-225). (Lecture Notes in Computational Science and Engineering; Vol. 98). Springer-Verlag. https://doi.org/10.1007/978-3-319-05789-7_18
El Bouajaji, Mohamed ; Dolean, Victorita ; Gander, Martin J. ; Lanteri, Stéphane ; Perrussel, Ronan. / DG discretization of optimized Schwarz methods for Maxwell's equations. Domain Decomposition Methods in Science and Engineering XXI. editor / Jocelyne Erhel ; Martin J. Gander ; Laurence Halpern ; Géraldine Pichot ; Taoufik Sassi ; Olof Widlund. Vol. 98 Springer-Verlag, 2014. pp. 217-225 (Lecture Notes in Computational Science and Engineering).
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El Bouajaji, M, Dolean, V, Gander, MJ, Lanteri, S & Perrussel, R 2014, DG discretization of optimized Schwarz methods for Maxwell's equations. in J Erhel, MJ Gander, L Halpern, G Pichot, T Sassi & O Widlund (eds), Domain Decomposition Methods in Science and Engineering XXI. vol. 98, Lecture Notes in Computational Science and Engineering, vol. 98, Springer-Verlag, pp. 217-225, 21st International Conference on Domain Decomposition Methods in Science and Engineering, DD 2014, Rennes, France, 25/06/12. https://doi.org/10.1007/978-3-319-05789-7_18

DG discretization of optimized Schwarz methods for Maxwell's equations. / El Bouajaji, Mohamed; Dolean, Victorita; Gander, Martin J.; Lanteri, Stéphane; Perrussel, Ronan.

Domain Decomposition Methods in Science and Engineering XXI. ed. / Jocelyne Erhel; Martin J. Gander; Laurence Halpern; Géraldine Pichot; Taoufik Sassi; Olof Widlund. Vol. 98 Springer-Verlag, 2014. p. 217-225 (Lecture Notes in Computational Science and Engineering; Vol. 98).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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El Bouajaji M, Dolean V, Gander MJ, Lanteri S, Perrussel R. DG discretization of optimized Schwarz methods for Maxwell's equations. In Erhel J, Gander MJ, Halpern L, Pichot G, Sassi T, Widlund O, editors, Domain Decomposition Methods in Science and Engineering XXI. Vol. 98. Springer-Verlag. 2014. p. 217-225. (Lecture Notes in Computational Science and Engineering). https://doi.org/10.1007/978-3-319-05789-7_18